Fast and Robust Graph-based Transductive Learning via Minimum Tree Cut

In this paper, we propose an efficient and robust algorithm for graph-based transductive classification. After approximating a graph with a spanning tree, we develop a linear-time algorithm to label the tree such that the cut size of the tree is minimized. This significantly improves typical graph-based methods, which either have a cubic time complexity (for a dense graph) or $O(kn^2)$ (for a sparse graph with $k$ denoting the node degree). %In addition to its great scalability on large data, our proposed algorithm demonstrates high robustness and accuracy. In particular, on a graph with 400,000 nodes (in which 10,000 nodes are labeled) and 10,455,545 edges, our algorithm achieves the highest accuracy of $99.6\%$ but takes less than $10$ seconds to label all the unlabeled data. Furthermore, our method shows great robustness to the graph construction both theoretically and empirically, this overcomes another big problem of traditional graph-based methods. In addition to its good scalability and robustness, the proposed algorithm demonstrates high accuracy. In particular, on a graph with $400,000$ nodes (in which $10,000$ nodes are labeled) and $10,455,545$ edges, our algorithm achieves the highest accuracy of $99.6\%$ but takes less than $10$ seconds to label all the unlabeled data.